Finite-element method simulation of effects of microstructure, stress state, and interface strength on flow localization
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I. INTRODUCTION
MANY in situ composites are candidate materials for high-temperature aerospace applications.[1–19] Examples of these in situ composites include Nb-Ti-Hf-Cr-Al-Si,[2–5] NbCr-Ti-Al,[9,10] Nb-Cr-Ti,[11–16] Nb-Al-Ti,[7,8] and Mo-SiB[17,18,19] systems. The main characteristics of these in situ composites are (1) a large volume fraction of intermetallic particles that are intended to provide high-temperature strength, creep strength, and oxidation resistance; and (2) a ductile solid-solution-alloy matrix that is intended to provide tensile ductility and fracture resistance at ambient temperatures. None of the current in situ composites exhibit all the desired mechanical properties for applications at or above 1200 8C, but the Nb-Ti-Hf-Cr-Al-Si system[2–5] is by far the most developed in situ composite system. The fatigue and fracture characteristics of many in situ composites have been identified. Some of the important features associated with fracture of Nb-Cr-Ti in situ composites are particle fracture and flow localization in the ligament between cracked particles or microcracks.[12,13,14] The microstructure of the in situ composite Nb-36Cr-27Ti, which contains 38 pct Cr2Nb particles in a Nb-Cr-Ti solid-solution matrix, is shown in Figure 1(a). The composite contained a crack (left side) that was loaded to a stress intensity, K, level of '20 MPa!m. Several of the Cr2Nb particles located ahead of the crack tip were cracked as the result of the crack-tip stress field. The near-tip strain distribution is illustrated in Figure 1(b), which depicts the concentration of strain in a ligament located between the tip of the main crack and a cracked particle in the Nb-Cr-Ti solid-solution matrix.[12] It is evident from Figure 1 that the plastic strain is localized within a small deformation zone. Because of GUOYU LIN, formerly with the GKSS Research Center, Geesthacht, Germany, is with ANSYS, Canonsburg, PA 15317. KWAI S. CHAN, Institute Scientist, is with the Southwest Research Institute, San Antonio, TX 78238. Manuscript submitted February 22, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
strain localization, the ligament fractured relatively easily and did not provide sufficient bridging force or plastic dissipation to improve fracture resistance. Thus, for fracture toughness considerations, it would be desirable to eliminate or delay particle fracture in in situ composites containing hard particles. Qualitatively, both particle fracture and flow localization in the matrix ligament can be explained on the basis of a high plastic constraint due to a buildup of the triaxial tensile stress arising from maintaining compatibility between the nondeformable particles and the deformable matrix. Experimental measurements of local strains in in situ composites indicated a high constraint near the hard particles.[20] This information alone, however, is insufficient for devising a means for reducing the plastic constraint to eliminate particle fracture, to reduce flow localization, and to enhance plastic dissipation in
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